Optimal. Leaf size=25 \[ \frac {\left (a x^3+b x^6\right )^{5/3}}{5 b x^5} \]
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Rubi [A]
time = 0.00, antiderivative size = 25, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {2025}
\begin {gather*} \frac {\left (a x^3+b x^6\right )^{5/3}}{5 b x^5} \end {gather*}
Antiderivative was successfully verified.
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Rule 2025
Rubi steps
\begin {align*} \int \left (a x^3+b x^6\right )^{2/3} \, dx &=\frac {\left (a x^3+b x^6\right )^{5/3}}{5 b x^5}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 25, normalized size = 1.00 \begin {gather*} \frac {\left (x^3 \left (a+b x^3\right )\right )^{5/3}}{5 b x^5} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.13, size = 29, normalized size = 1.16
method | result | size |
gosper | \(\frac {\left (b \,x^{3}+a \right ) \left (b \,x^{6}+a \,x^{3}\right )^{\frac {2}{3}}}{5 b \,x^{2}}\) | \(29\) |
trager | \(\frac {\left (b \,x^{3}+a \right ) \left (b \,x^{6}+a \,x^{3}\right )^{\frac {2}{3}}}{5 b \,x^{2}}\) | \(29\) |
risch | \(\frac {\left (x^{3} \left (b \,x^{3}+a \right )\right )^{\frac {2}{3}} \left (b \,x^{3}+a \right )}{5 x^{2} b}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 14, normalized size = 0.56 \begin {gather*} \frac {{\left (b x^{3} + a\right )}^{\frac {5}{3}}}{5 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 28, normalized size = 1.12 \begin {gather*} \frac {{\left (b x^{6} + a x^{3}\right )}^{\frac {2}{3}} {\left (b x^{3} + a\right )}}{5 \, b x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \left (a x^{3} + b x^{6}\right )^{\frac {2}{3}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.15, size = 29, normalized size = 1.16 \begin {gather*} \frac {\left (\frac {a}{5\,b}+\frac {x^3}{5}\right )\,{\left (b\,x^6+a\,x^3\right )}^{2/3}}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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